GAP implementation

Group ID

This finite group has order 18 and has ID 3 among the groups of order 18 in GAP's SmallGroup library. For context, there are groups of order 18. It can thus be defined using GAP's SmallGroup function as:

SmallGroup(18,3)

For instance, we can use the following assignment in GAP to create the group and name it :

gap> G := SmallGroup(18,3);

Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [18,3]

or just do:

IdGroup(G)

to have GAP output the group ID, that we can then compare to what we want.